with \(i_0, \ldots , i_n \in \Lambda \)  is either empty or a cartesian space.
(For \(F \in {H}_\infty \)  we set \(F(\emptyset ) = *\) , in accordance with the Yoneda Lemma and \(\underline{{H}}_\infty (\emptyset , F) = *\) , where here \(\emptyset \in {H}_\infty \)  is the initial object.)
We let \(\ell \)  denote the class of Čech coverings in \({H}_\infty \)  with respect to the Grothendieck pretopology \(\tau \) .
Given a simplicial model category \({{M}}\)  and a class \(S\)  of morphisms in \({{M}}\) , we denote by \(L_S {{M}}\)  the simplicially enriched left Bousfield localisation of \({{M}}\)  at the morphisms in \(S\)  (see [1]} for more background).
